# World of Tan 28 - Concentrating on Coordinates

Can you fit the tangram pieces into the outline of the playing piece?

This activity follows on from World of Tan 27 - Sharing.

On the table, there is a sheet of paper covered with dots. Little Ming and Little Fung are using it to play a game.

It is almost time for dinner and Granma T is busy preparing the meal. She keeps asking Little Ming and Little Fung to clear the table and set out bowls and chopsticks, but they are focused on their game and don't seem to hear her...

**Granma T:**For the last time, you two need to move and set the table!

The two children jump in suprise and rush to get ready for dinner.

**Little Ming:**We were only doing our homework.

**Little Fung:**And I was winning!

**Granma T:**Well perhaps while we eat dinner you can explain what has kept you so engrossed. Mah Ling and Chi Ping have been playing this game all afternoon, and the workers appear to have forgotten they come here to work.

**Little Ming:**It's a game that we've been taught at school.

**Little Fung:**To help us learn all about coordinates.

**Granma T:**Ah, I remember learning about coordinates! You mean a point P (x,y). That takes me back - now, what did we call them back then?

**Little Fung:**Call what?

**Granma T:**An ordered sequence of two numbers that locate a point on a grid - the plane.

**Little Ming:**Plain! What do you mean?

**Granma T:**Yes, a point on the plane and an ordered sequence of three numbers locates a point in space.

**Little Fung:**No, no Granma T! This is just a game on a grid. We'll show you after supper - you might like to play!

**Granma T:**And is this the game that everyone in the yard has been playing?

**Little Ming:**I'm afraid so, but there wasn't much work to do anyway!

**Granma T:**So I am paying others to play games? Even Mah Ling was playing, wasn't she? Let's eat now, then we can take a proper look at this game after dinner.

In the meantime, complete the silhouette of one of the playing pieces from chess, which is Little Ming's favourite game.

Extra activities:

- Have a go at Little Ming and Little Fung's game here.
- Find out which mathematician 'invented' the idea of coordinates.

The story continues in World of Tan 29 - The Telephone.

### Why do this problem?

This problem is an engaging context in which pupils can consolidate their knowledge of the properties of squares, triangles and parallelograms. By attempting this activity, children will be putting into practise their visualising skills, making guesses about where the different shapes might go before trying out their ideas. When combining the shapes to make the tangram, pupils will use their understanding of translations, reflections and rotations to decide how to transform each shape. There are also links between tangrams and fractions, and children can be encouraged to work out what fraction of the whole square is represented by each smaller shape.### Possible approach

Read this story with the whole class and look at the tangram as a group. Ask pupils to suggest where a shape might go. What transformation would be needed to move the shape into that position?When pupils are solving the tangram, they would benefit from working in pairs with a tablet or a printed copy of the shapes to cut out and move around. Working together will lead to rich discussions about the possible options for where each shape can go. When the children have solved the tangram, they can have a go at the extra activities.

At the end of the lesson, bring all of the pupils together and model the solution on the whiteboard. How does each shape need to be transformed? What fraction of the whole picture is each shape?

### Key questions

What could you put with this piece to make a square?Are all of the pieces different?

What's the smallest square you can make?

What has to go in that space? How do you know?